We develop a closed-form Haseman-Elston estimator for genetic and environmental correlation coefficients between complex phenotypes, which we term HEc, that is as precise as GCTA yet ∼20× faster. We estimate genetic and environmental correlations between over 7,000 phenotype pairs in subgroups from the Trans-Omics in Precision Medicine (TOPMed) program. We demonstrate substantial differences in both heritabilities and genetic correlations for multiple phenotypes and phenotype pairs between individuals of self-reported Black, Hispanic/Latino, and White backgrounds. We similarly observe differences in many of the genetic and environmental correlations between genders. To estimate the contribution of genetics to the observed phenotypic correlation, we introduce “fractional genetic correlation” as the fraction of phenotypic correlation explained by genetics. Finally, we quantify the enrichment of correlations between phenotypic domains, each of which is comprised of multiple phenotypes. Altogether, we demonstrate that the observed correlations between complex human phenotypes depend on the genetic background of the individuals, their gender, and their environment
